In the figure above, ED has a length of 4. What is the length of side AC?
1) The perimeter of triangle EBD is 20.
2) Side AE = 8.
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Statement 1
Perimeter of EBD is 20 . Triangle EBD in an isosceles triangle. Hence
\(EB=BD=\frac{(Perimeter -ED)}{2}\)
=\(\frac{(20-4)}{2}\) =8
Also triangle ABE and Triangle BDC are congruent, Hence AE= CD
Also in Triangle AEB , \(Angle ABE =\frac{(180-2x-(180-4x))}{2}=\frac{2x}{2}=x\)
Hence AE=EB=8
Also as AE=CD
Hence, AC= AE+ED+CD= 8+4+8= 20 (
Hence, Statement 1 alone is sufficient)Statement 2
AE=8
As triangle ABE and Triangle BDC are congruent, Hence AE= CD
Hence AC= AE+ED+CD= 8+4+8= 20 (
Hence, Statement 2 alone is also sufficient)Hence the answer is D, Each statement alone is sufficient to answer the question
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